相关论文: Algebraic automatic continued fractions in charact…
We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average…
First we generalize the Thue-Morse sequence (the generalized Thue-Morse sequences) by a cyclic permutations and p-adic system, and consider the necessary-sufficient condition that it is non-periodic. Moreover if the generalized Thue-Morse…
Let G be a reductive p-adic group, H(G) its Hecke algebra and S(G) its Schwartz algebra. We will show that these algebras have the same periodic cyclic homology. This might be used to provide an alternative proof of the Baum-Connes…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
Automatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation measure of order 2 is large. These sequences are highly…
Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…
Let A be a finite subset of the natural numbers containing 0, and let f(n) denote the number of ways to write n in the form $\sum e_j2^j$, where $\e_j \in A$. We show that there exists a computable T = T(A) so that the sequence (f(n) mod 2)…
We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers a so that either (a, a^2) or (a,…
Most well-known multidimensional continued fractions, including the M\"{o}nkemeyer map and the triangle map, are generated by repeatedly subdividing triangles. This paper constructs a family of multidimensional continued fractions by…
Casually introduced thirty years ago, a simple algebraic equation of degree 4, with coefficients in Fp[T], has a solution in the field of power series in 1/T, over the finite field Fp. For each prime p > 3, the continued fraction expansion…
We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out…
Currie and Saari initiated the study of least periods of infinite words, and they showed that every integer n >= 1 is a least period of the Thue-Morse sequence. We generalize this result to show that the characteristic sequence of least…
In this paper we describe the group of symmetries of a two-dimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra. We distinguish two types of symmetries: the Dirichlet-type…
We prove a two-parameter family of continued fraction identities for $\arctan(p/q)$, where $p$ and $q$ are positive integers with $p\le q$. For every such pair, the identity \[ \arctan\frac{p}{q} =…
In this article, first we generalize the Thue-Morse sequence $(a(n))_{n=0}^\infty$ (the generalized Thue-Morse sequences) by a cyclic permutation and $k$ -adic expansion of natural numbers, and consider the necessary-sufficient condition…
We demonstrate that discrete m-functions with eventually periodic continued fraction coefficients have an algebraic relationship to their second solution if and only if the periodic part of the sequence of continued fraction coefficients is…
We consider series of the form $$ \frac{p}{q} +\sum_{j=2}^\infty \frac{1}{x_j}, $$ where $x_1=q$ and the integer sequence $(x_n)$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for $n\geq 1$.…
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued…
We consider a special class of periodic continued fractions (called alpha-fractions) and discuss the related algebraic and geometric problems. A classical description of the Jacobi variety of a hyperelliptic curve due to Jacobi naturally…
In this article we introduce a new approach to compute infinite products defined by automatic sequences involving the Thue-Morse sequence. As examples, for any positive integers $q$ and $r$ such that $0 \leq r \leq q-1$, we find infinitely…